Is there a hotkey for making a face from the inner outline I did in this picture?
Select all inner edges (like on screenshot), then go to Mesh - Faces - Fill (Alt+F), it will fill all with Triangles, selecting all of them. To turn Most of them into Quads, go to Mesh - Faces - Tris To Quads (Alt+J). 
If there's any Triangles left - dissolve their edges, and then just continue the needed loopcuts through created faces, where needed (mostly at the place, where Triangle's edges were dissolved) with Knife tool (K).

I'm pretty shure that there's a better method, but this will work, too.